Where AGI Confuses Change: A Recurrence–Structure Diagnostic for Autonomous Self-Improvement Claims in Artificial Intelligence

Artificial General Intelligence (AGI) discourse frequently interprets capability growth as evidence of structural change in machine intelligence. However, many claims of “recursive self-improvement” fail to explicitly declare the recurrence conditions under which such structural change could be evaluated. This paper introduces a recurrence–structure diagnostic grounded in the KOGNETIK framework. The method separates state variation (Δx) from rule-class mutation (ΔS) under declared recurrence conditions and enforces Rule–State Separation (RSSA) as a structural admissibility gate. The protocol requires explicit declaration of: recurrence operator (R), structure object defined as an equivalence class of rule-objects (S := g~), rule–state separation conditions (RSSA), structural regime output (Ψ). Applying this diagnostic reveals that many AGI self-improvement narratives resolve either into state variation within a fixed rule class (Ψ = 0) or into structural undecidability when recurrence and structure are not formally declared. The contribution of this paper is methodological rather than evaluative: it provides a reproducible audit protocol that research laboratories can use to test structural claims about AI systems under explicit recurrence conditions. Intellectual Property & Licensing The KOGNETIK Research Series is released under the Creative Commons Attribution–NonCommercial 4.0 International License (CC BY-NC 4.0). All scientific works within the series may be cited, shared, and adapted for non-commercial research purposes with proper attribution. Commercial use—including consulting, advisory services, integration into commercial platforms, monetized training, certification, or system-level deployment—is not permitted under this license and requires a separate written agreement. Full license text:https://creativecommons.org/licenses/by-nc/4.0/ For licensing, partnerships, translations, or applied development inquiries:research@kognetik.dehttps://www.kognetik.de ORCID: https://orcid.org/0009-0000-8544-4847 Kognetik Series Information KOGNETIK — Minimal Operator Definition of Reflexivity (Ψ = ∂S/∂R) Reflexivity as structural rate-of-change:Ψ = ∂S/∂R measures structural drift under recurrence. Process, not state:Reflexivity specifies a transformation rule rather than a content or level. Domain-independent operator:Applicable across biological, cognitive, artificial, social, industrial, and geophysical systems. Non-ascriptive and empirically testable:Ψ enables comparative analysis of systems via observable structure and recurrence. Higher-order phenomena as specifications:Learning, adaptation, consciousness, governance, and identity are structured regimes of Ψ.